As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi-mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain-hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.